\newproblem{lay:2_1_27}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.1.27}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Let $\mathbf{u}=\begin{pmatrix}-3\\2\\-5\end{pmatrix}$ and $\mathbf{v}=\begin{pmatrix}a\\b\\c\end{pmatrix}$. Compute $\mathbf{u}^T\mathbf{v}$, $\mathbf{v}^T\mathbf{u}$,
	$\mathbf{u}\mathbf{v}^T$ and $\mathbf{v}\mathbf{u}^T$.
}{
  % Solution
	\begin{center}
		$\begin{array}{rcl}
			\mathbf{u}^T\mathbf{v}&=&\begin{pmatrix}-3 &2&-5\end{pmatrix}\begin{pmatrix}a\\b\\c\end{pmatrix}=-3a+2b-5c\\
			\mathbf{v}^T\mathbf{u}&=&\begin{pmatrix}a&b&c\end{pmatrix}\begin{pmatrix}-3\\2\\-5\end{pmatrix}=-3a+2b-5c\\
			\mathbf{u}\mathbf{v}^T&=&\begin{pmatrix}-3\\2\\-5\end{pmatrix}\begin{pmatrix}a&b&c\end{pmatrix}=\begin{pmatrix}-3a&-3b&-3c\\2a&2b&2c\\-5a&-5b&-5c\end{pmatrix}\\
			\mathbf{v}\mathbf{u}^T&=&\begin{pmatrix}a\\b\\c\end{pmatrix}\begin{pmatrix}-3&2&-5\end{pmatrix}=\begin{pmatrix}-3a&2a&-5a\\-3b&2b&-5b\\-3c&2c&-5c\end{pmatrix}\\
		\end{array}$
	\end{center}
}
\useproblem{lay:2_1_27}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
